Adaptive dual polarized mimo for dynamically moving transmitter and receiver

ABSTRACT

Systems and methods are presented for increasing throughput between mobile transmitters/receivers (e.g., between an Unmanned Aerial Vehicle and a ground station) using orthogonally polarized transmission channels. The system may first calibrate the receiver and transmitter antenna pairs using pilot signals and then may update look up tables for feedforward correction. The system may decouple and predict the cross polarization interference due to relative dynamic movement between the transmitter and the receiver. The system may perform a closed-loop suboptimal estimation to generate refined corrections by minimizing a difference between a training vector and a pilot-signal feedback. Cross-polarization discrimination between the transmission and reception antennas may then be Cancelled to improve signal to noise and interference ratio and performance of the system.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of and claims priority to commonlyassigned U.S. patent application Ser. No. 14/852,987, entitled “ADAPTIVEDUAL POLARIZED MIMO FOR DYNAMICALLY MOVING TRANSMITTER AND RECEIVER”,which was filed Sep. 14, 2015, which disclosure is incorporated byreference herein in its entirety.

TECHNICAL FIELD

The disclosed embodiments relate to wireless communication usingpolarized antenna systems.

BACKGROUND

Dual polarized feed antennas transmit and receive electromagneticsignals in two orthogonal special domains. Such configurations can beespecially useful for wireless communication links where transmittersand receivers are constrained for power or weight, e.g., an unmannedaerial vehicle (UAV) enabled high altitude platform (HAP) links. Forexample, when communicating between an aerial device, e.g., a UAV, and aground station or a peer aerial device, a dual polarized antennacommunication system could double the throughput without usingadditional antenna and associated tracking system. However due to themaneuvering moving of a UAV, the orthogonality is difficult to maintainand the RXs are degraded dramatically, the applications using dualpolarized feed antennas have generally been limited to fixedpoint-to-point communications. Cross-polarization discrimination (XPD)resulting from non-ideal antenna implementations, channel distortionresulting from atmospheric propagation, and aerial vehiclemaneuverability each adversely impact the achievable Signal-to-NoiseRatio (SNR). Until these factors are adequately addressed, dualpolarized feed antennas' applicability in a dynamic context will belimited.

BRIEF DESCRIPTION OF THE DRAWINGS

The techniques introduced here may be better understood by referring tothe following Detailed Description in conjunction with the accompanyingdrawings, in which like reference numerals indicate identical orfunctionally similar elements:

FIG. 1A is a block diagram illustrating a vertically polarized signal asmay be implemented in some embodiments; FIG. 1B is a block diagramillustrating a horizontally polarized signal as may be implemented insome embodiments;

FIG. 2 is a plot of an example of the Signal-to-Noise-Ratio (SNR) Marginrelative to the percentage of cross polarization coupling as may beconsidered in some embodiments;

FIG. 3A is block diagram illustrating various variables and componentsrelevant to some embodiments; FIG. 3B is block diagram illustrating theeffects of cross-polarization as may occur in some embodiments; FIG. 3Cis block diagram illustrating orientations corresponding to variousvariables referenced in some embodiments;

FIG. 4 is a series of equations associated with factors assessed incertain embodiments;

FIG. 5 is a series of equations associated with cross-polarizationfactors assessed in certain embodiments;

FIG. 6 is a series of equations reflecting signal processing as may beconsidered in some embodiments;

FIG. 7 is a flow diagram illustrating steps in a cross-polarizationcalibration and reassessment process as may be considered in someembodiments;

FIG. 8 is a flow diagram illustrating steps in a cross-polarizationcalibration and reassessment process as may be considered in someembodiments;

FIG. 9 is a block diagram illustrating components in across-polarization calibration and reassessment system as may beconsidered in some embodiments;

FIG. 10 is a block diagram illustrating transmission-side components ina cross-polarization calibration and reassessment system as may beconsidered in some embodiments;

FIG. 11 is a block diagram illustrating reception-side components in across-polarization calibration and reassessment system as may beconsidered in some embodiments; and

FIG. 12 is a block diagram of a computer system as may be used toimplement features of some of the embodiments.

While the flow and sequence diagrams presented herein show anorganization designed to make them more comprehensible by a humanreader, those skilled in the art will appreciate that actual datastructures used to store this information may differ from what is shown,in that they, for example, may be organized in a different manner; maycontain more or less information than shown; may be compressed and/orencrypted; etc.

The headings provided herein are for convenience only and do notnecessarily affect the scope or meaning of the claimed embodiments.Further, the drawings have not necessarily been drawn to scale. Forexample, the dimensions of some of the elements in the figures may beexpanded or reduced to help improve the understanding of theembodiments. Similarly, some components and/or operations may beseparated into different blocks or combined into a single block for thepurposes of discussion of some of the embodiments. Moreover, while thevarious embodiments are amenable to various modifications andalternative forms, specific embodiments have been shown by way ofexample in the drawings and are described in detail below. Theintention, however, is not to limit the particular embodimentsdescribed. On the contrary, the embodiments are intended to cover allmodifications, equivalents, and alternatives falling within the scope ofthe disclosed embodiments as defined by the appended claims.

DETAILED DESCRIPTION

Systems and methods are presented for increasing throughput betweenmobile transmitters/receivers (e.g., between an Unmanned Aerial Vehicle(UAV)/Unmanned Aerial System (UAS) and a ground station) usingorthogonally polarized transmission channels. The system may firstcalibrate the receiver and transmitter antenna pairs using pilot signalsbefore motion. Note that each of the UAV and ground station may have atransmitter and receiver corresponding to a receiver and transmitter atits counterpart. Similarly, though some examples described herein willrefer to the UAV or ground station as the “transmitter” or “receiver”one will readily recognize that the roles could be reversed. The systemmay then provide suboptimal estimation correction by minimizing adifference between a training vector and a pilot-signal determinedchannel matrix. Cross-polarization discrimination between the antennasmay then be determined. Bayesian methods may also be applied in someembodiments to modify the channel matrix in use. Specific architecturesfor implementing the above-referenced method at the transmitting andreceiving devices are also provided.

Various examples of the disclosed techniques will now be described infurther detail. The following description provides specific details fora thorough understanding and enabling description of these examples. Oneskilled in the relevant art will understand, however, that thetechniques discussed herein may be practiced without many of thesedetails. Likewise, one skilled in the relevant art will also understandthat the techniques can include many other obvious features notdescribed in detail herein. Additionally, some well-known structures orfunctions may not be shown or described in detail below, so as to avoidunnecessarily obscuring the relevant description.

The terminology used below is to be interpreted in its broadestreasonable manner, even though it is being used in conjunction with adetailed description of certain specific examples of the embodiments.Indeed, certain terms may even be emphasized below; however, anyterminology intended to be interpreted in any restricted manner will beovertly and specifically defined as such in this section.

Overview

FIG. 1A is a block diagram illustrating a vertically polarized signal asmay be implemented in some embodiments. An idealized antenna 110 may beoriented so as to be parallel with a z-axis in a given reference frame.Radiation emitted from this antenna 115 may accordingly be polarizedalong the z-axis and will ideally retain such polarization whenintersecting a distant surface 120. Accordingly, a receiving antenna atthe position of surface 120 would receive the entirety of the polarizedsignal if it was likewise configured to receive the signal along thez-axis (i.e., orientation 105 b). At a relative 45 degree rotation,corresponding to each of orientations 105 a and 105 c, the signal 115would be received at approximately half the strength. At an orientationrotated at 90 degrees, e.g., an orientation 105 d, none of the signal115 would be received.

Conversely, FIG. 1B is a block diagram illustrating a horizontallypolarized signal 130 emitted from an antenna 125 in a correspondingconfiguration. In this case, a receiver in orientation 105 d wouldreceive all of signal 130, a receiving antenna in either of orientations105 a and 105 c would receive signal 130 at half strength, and areceiving antenna in orientation 105 b would receive none of signal 130.In some embodiments of a transmission and reception system in which dualpolarized antennas are used, two independent signals may be transmittedand received concurrently. These two transmitted signals, represented asa first component Uh and a second component Uv that is orthogonal to thefirst component (i.e., Uv·Uh=0) may be fed through orthogonal polarizedelectromagnetic antenna elements. For example, Uv can be vertical forlinearly polarized or left for circular polarized component, and Uh isthe orthogonal counterpart of Uv, which is the horizontal for linearlypolarized or the right left component for circular polarized signals. Insuch systems, cross-polarization discrimination (XDP) may thus refer toa component of Uv projected in the direction of Uh, or a component of Uhprojected in the direction of Uv, and thus may result in a receiverreceiving the projection component of Uh along with the signal Uv orcomponent of Uv in the direction of Uh, along with Uh, which may seem tobe interference to the receiver.

As discussed, cross-polarization discrimination (XPD) resulting fromnon-ideal antenna implementations, channel distortion resulting fromatmospheric propagation, and aerial vehicle maneuverability may eachadversely impact the achievable Signal-to-Noise Ratio (SNR). FIG. 2 is aplot of the SNR Margin relative to the percentage of cross polarizationcoupling. As the data rate and power increase, the degradation likewiseincreases. To address this problem, various embodiments correct for theXPD in transmission and/or reception to enable the use of dual polarizedfeed antennas.

System Model—Mathematical Model

Various embodiments consider transmission and reception systems eachhaving orthogonally polarized antenna pairs. FIG. 3A is a block diagramillustrating various variables and components relevant to someembodiments. A transmitter may have a vertically polarized 305 a and ahorizontally polarized 305 b antenna. The receiver may then receive thesignal from across the channel using vertically polarized antenna 310 aand horizontally polarized antenna 310 b. The cross-polarization anglebetween the antennas at the transmitter is reflected by ξ_(t) (andlikewise ξ_(r) for the receiver). As discussed in greater detail withrespect to FIG. 5, each of ξ_(t) and may be decomposed into itsconstituent contributions to the cross-polarization across the channel.These effects may be embodied for the transmitter in a base matrixA_(t), a cross-polarization matrix ΔC_(t), and a base cross-correlationmatrix B_(t) with similar counterparts at the receiver. When the anglebetween one received orthogonal component Uvr and the correspondingtransmitted component Uht is 90 degrees, and the received otherorthogonal component Uhr and the transmitted other orthogonal componentUvt is 90 degree, then the polarization components meet theorthogonality condition Uv·Uh=0, and may be referred to as matched Uvand U. When a difference of an angle ξ occurs, the dual polarizedtransmissions/receptions (TRXs) are not matched. The mismatch angleξ_(t) and ξ_(r) denote the delta angle offset from 90 degree for the twoorthogonal components.

FIG. 3B is block diagram illustrating the effects of cross-polarizationas may occur in some embodiments. In situation 325 a, the transmitterand receivers may be properly aligned such that no cross-polarizationresults. That is, the vertical A signal arrives at the vertical Cantenna without interference from the horizontal B signal and thehorizontal B signal arrives at the horizontal D antenna withoutinterference from the vertical A signal. In situation 325 b, thetransmitter and receivers are misaligned at a roughly 45 degree angleand accordingly portions of the A signal are appearing on both antennasD and D. In situation 325 c, the transmitter and receivers are at 90degree angles and consequently the signals are completelycross-polarized.

FIG. 3C is block diagram illustrating orientations corresponding tovarious variables referenced in some embodiments. As indicated, φ_(t),Y_(t), and θ_(t) reflect the respective orientations of the transmitterto the receiver. In FIG. 3A, FIG. 3B and FIG. 3C, the instantaneous Uvand Uh for an earth station can be described using the earthcoordinates, and the instantaneous Uv and Uh for a UAV can be describedusing UAV body coordinates with the corresponding attitudes that arewell defined in literature

System Model—Mathematical Model—Channel Modeling Equations

FIG. 4 is a series of equations associated with factors assessed incertain embodiments. Generally speaking, a distorted signal 405,received at the receiver may be generated by applying a transformationmatrix 410 to the originally transmitted signal 415. The transformationmatrix 410 may reflect the channel's contribution to the distortion aswell as the antenna polarization's contribution at each of thetransmitters and receivers. These effects are decomposed into the moreexplicit series of equations 420 a, 420 b, and 420 c. Equation 420 bsimply reflects the effect of the channel 425 on the transmitted signal.The matrices A_(t) and A_(r) generally reflect the cross polarizationeffect of the antennas at each of the transmitter and receiver. Thesematrices can be more thoroughly decomposed into their components asreflected in equation 430, which shows the signal interferencecomponents due to XPD distortion.

FIG. 5 is a series of equations associated with cross-polarizationfactors assessed in certain embodiments. Antenna polarization mismatchis partitioned into three parts in static mismatch ξ_(h0), the dynamicmismatch ξ _(v) due to UAV moving, and the random projections Δξ_(h) dueto external physical factors such as the channel and wind, etc.Particularly, equation 430 may be more thoroughly decomposed byrecognizes that the horizontal ξ_(h) and vertical ξ_(v)cross-polarization components may be decomposed into: an initialcomponent 510 a, 510 b; a time variable component 515 a, 515 b; and anoffset component 520 a, 520 b, showing the mismatch components. Theinitial component 510 a, 510 b and time variable component 515 a, 515 bmay be grouped into a single base component 525 a, 525 b. In thismanner, equation 420 c may be rewritten as equation 530 that de-couplesthe mismatch sources as having base matrix A_(t), a cross-polarizationmatrix ΔC_(t), and a base cross-correlation matrix B_(t), thus showingnonlinear XPD due to initial and UAV dynamic movement and linear randommismatch sources. A counterpart equation exists for the receiver sidemay be written in an analogous manner.

FIG. 6 shows an example of an algorithm that implements the nonlinearUAV moving dynamic invoked prediction of the XPD interference. Anexample that uses this algorithm can be implemented in three steps. Thefirst step is the stationary open loop from the a priori and lookuptable. The second step is the UAV flight dynamic involved nonlinearprediction. The third step is Bayes optimal closed loop correction. Thethree steps are represented in equations 605, 610, and 615 respectively,reflecting signal processing as may be considered in some embodimentsbased on the results of FIGS. 4 and 5. Equation 605 provides an exampleof how to estimate the initial and stationary interference, i.e., thebehavior when both the transmitter and receiver are stationary. Equation610 reflects the behavior when both the transmitter and receiver aremoving, e.g., dynamic prediction and optical estimation with UAV movingdynamics. Equation 615 reflects a recursive Bayesian process with thesame behavior as in equation 610, but with the terms reordered.

Example Channel and Cross-Polarization Compensation Process

Given the representation of FIG. 6 various embodiments present methodsfor determining intermediate components to facilitate a more generalrecovery of the source transmission at the receiver. FIG. 7 is a flowdiagram illustrating steps in a cross-polarization calibration andreassessment process as may be considered in some embodiments. At block705, each of the transmitter and receiver systems may define commonorthogonal planes. At block 710, the transmitter may pre-calibrate tothe expected antenna depolarization angle. At block 715, the receivermay likewise pre-calibrate to the expected antenna depolarization angle.

At block 720, each of the transmitter and receiver may set an a priorichannel matrix H₀, e.g., as determined from an almanac table lookup,past operations, etc. At block 725, the receiver may estimate thetransmitter's attitude/mapping with the antenna tracking angle. Thesystem may predict the depolarization angle and calculate the A_(t) andB_(t) matrices.

At block 730, the transmitter may estimate the receiver'sattitude/mapping with the antenna tracking angle, predict depolarizationangle, and calculate A_(r), B_(r) matrices. At block 735, the receiversystem may make level I correction sub-optimal estimation in bothpolarization domains. At block 740, the transmitter may transmit, andthe receiver may detect, channel pilot signals which are used toestimate the small cross-polarization ΔC_(t), ΔC_(r), using A_(r) ^(T),A_(t), H, S, and U (e.g., using maximum likelihood estimation). At block745, the system may apply post-corrected H conditions on ΔC_(t), ΔC_(r),A_(r) ^(T), A_(t), S, and U (e.g., using Bayesian Estimation). At block750, the receiver may process received signals U to determine signals S.If iterative assessments are to continue at block 755, then the systemmay repeat the operations beginning at block 725.

FIG. 8 is a flow diagram illustrating steps in a cross-polarizationcalibration and reassessment process as may be considered in someembodiments. At block 805 a, the transmitter may initialize a channelmatrix H, e.g., using an almanac as described above. At block 810 a, thetransmitter may perform an initial calibration and verification of thetransmitter antenna with the selected reference coordinates and maycalculate depolarization angle (ξ₀, ζ₀). At block 815 a, the transmittermay set up the transmitter look-up tables (LUTs).

At block 820 a, the transmitter may determine the optimal receiverattitudes prediction based upon IMU data and GPS signals. At block 825a, the transmitter may use the LUTs to determine the optimal nonlinearestimation of the depolarization angles (ξ₀, ζ₀) based on estimatedattitudes. At block 830 a, the system may perform soft correctionthrough the method described above (some embodiments may assume there isno gimbal for low cost aerial receivers).

At block 840 a, the transmitter may process a received training reportand decision based on a training frame, power control, and modulationadaption. The results may be used to determine at block 835 a, ifcross-polarization discrimination training is to be performed. If notraining is to be performed, then normal transmissions may be performedat block 850 a. The training report may have been received whencross-polarization discrimination training feedback was detected atblock 860 a following reception at block 865 a (normal receptionoperations may occur at block 855 a, when no data is detected). At block820 b, the ground receiver may detect the cross-polarizationdiscrimination training signals and macro tracking.

At block 805 b, the receiver may also perform an initial calibration andverification of the receiver antenna with selected reference coordinatesand calculate depolarization angle (ξ₀, ζ₀). At block 810 b, thereceiver may setup the receiver LUTs.

Where training is to be performed, at block 845 a the transmitter mayenable MIMO channel training and transmit training signals and UASattitude signals. At block, 815 b the receiver may receive thecross-polarization discrimination training signals (where no suchsignals are present, normal reception may occur at block 830 b).

At block 825 b, the LUTs, cross-polarization discrimination trainingsignals and macro tracking may be used to determine an optimal estimateperturbation (Δξ_(α) Δ_(t)) and correct polarization angles (ξ_(α),ζ_(t)). If the criteria for hard correction are met at block 865 b, thenthe receiver may correct the ground antenna attitude at block 880 b,before performing soft correction at block 870 b. The correction may bereported to the ground station at block 875 b.

At block 835 b, the receiver may report the correction to thetransmitter. If the cross-polarization discrimination specifications aremet at block 855 b or if extended training is to be performed at block850 b, then the receiver may perform a feedback correction report,recommendation and/or acknowledge at block 845 b. At block 840 b, thereceiver may communicate with the transmitter.

Example Channel and Cross-Polarization Compensation System

FIG. 9 is a block diagram illustrating components in across-polarization calibration and reassessment system as may beconsidered in some embodiments. A transmitter 905 a may include a module910 to perform transmitter data and channel mapping and de-multiplexingto H and V channels. These may be based on a pilot signal 945 andTransmission correction parameters 955 a. The results may be provided toa Pre-Channel equalizer and System Nonlinearity Pre-distortion module935. The module may also receive priori LUTs 915 a andcross-polarization discrimination projection and estimation 920 aderived from antenna tracking 925 a.

The results may be used to generate dual polarized transmission signals940 which are placed on the antenna 930 a. These may be received at areceiver 905 b across a Propagation channel 950 at a dual polarizedreception antenna 930 b. The antenna may itself be oriented usingantenna tracking 925 b. Dual polarized reception signals 940 b may bederived and provided to each of a Timing & Synchronization & ChannelEstimation module 975 and a dual polarized MIMO De-MOD 970. The Timing &Synchronization & Channel Estimation module 975 may consider the resultsof the cross-polarization discrimination projection and estimationmodule 920 b.

An Equalizer and System distortion Correction module 990 may providecorrections to the Dual Polarized MIMO De-MOD 970 based on the prioriLUTs 915 b, transmission correction parameters 955 b, and the output ofTiming & Synchronization & Channel Estimation module 975. Dual PolarizedMIMO De-MOD 970 may then output the recovered Rx data 960.

FIG. 10 is a block diagram illustrating transmission-side components ina cross-polarization calibration and reassessment system as may beconsidered in some embodiments. To clarify the character of thecomponents depicted in FIG. 9, the transmitter's data and channelmapping and MUX 910 may receive pilot signals 1010 a, 1010 b as well asregular vertical 1005 a and horizontal 1005 b channel data.

Apriori LUTs 945 may include a prior antenna characterizationtransmission LUT 1015 a and a prior system transmission LUT 1015 b. ADual Polarized MIMO MOD 1015 may operate on data from the data andchannel mapping and MUX 910 and provide the results to the channelequalizer and system nonlinear pre-distortion module 935. Timing,location, IMU data 1020, transmission attitude detection data 1025, andtransmission antenna tracking angles or a given static angle, may beused with the antenna tracking data 925 a to inform thecross-polarization discrimination projection and estimation 920 a. Thechannel transmission may comprise horizontal 1020 b and vertical 1020 acomponents.

FIG. 11 is a block diagram illustrating reception-side components in across-polarization calibration and reassessment system as may beconsidered in some embodiments. Again, to be clear, each of a horizontalchannel signal 1125 a and a vertical channel signal 1125 b may bereceived from the receiver's antennas. The LUTs 915 b may include aprior system receiver LUT 1105 a and an apriori antenna characterizationreceiver LUT 1105 b. A Dual Polarization receiver Estimation module 1110may relay is results to the Equalizer and System distortion Correctionmodule 990. The received signal may be decomposed into a vertical datachannel 1120 a and a horizontal data channel 1120 b. A receiver up layerdata de-multiplexer and process module 1115 may ultimately generate therecovered transmission signal.

Timing and location IMU data 1135 and the receiving antenna's trackingand static angles 1130 may be used in conjunction with the antennatracking 980 to generate an input to the dual polarization receiver andestimation module 1110.

In some embodiments, a receiver communication device includes an antennaarrangement configured to concurrently receive and transmit twoindependent signals along two orthogonally polarized fields, over twoorthogonally polarized channels, at least one processor, and at leastone memory comprising instructions configured to cause the at least oneprocessor to determine an apriori channel matrix, estimate a transmitterbase matrix, and a transmitter base cross-correlation matrix, receive apilot signal from the two orthogonally polarized channels, estimate alocal cross-depolarization matrix and a transmitter cross-polarizationmatrix using the pilot signal, apply a post-correction channelcondition, receive a corrupted data signal from the two orthogonallypolarized channels, and estimate an original data signal by processingthe corrupted data signal using the transmitter base matrix, transmitterbase cross-correlation matrix, transmitter cross-polarization matrix,local base matrix, local base cross-correlation matrix, and localcross-depolarization matrix. In some embodiments, the antennaarrangement comprises a set of dual polarized antennas. In someembodiments, the antenna arrangement comprises one or more pairs ofseparately polarized antennas.

It will be appreciated by one of ordinary skill in the art thattechniques for receiving data transmissions in a communication systemhaving dual polarized channels are disclosed. It will also beappreciated by one of ordinary skill in the art that the disclosedtechniques are especially advantageous for embodiments in power andweight constrained communication systems such as for communication to orfrom a UAV enabled HAP. It will further be appreciated by one ofordinary skill in the art that data reception techniques can beimplemented in three steps: A first step is to implement a stationaryopen loop using the apriori knowledge and lookup tables. A second stepis to perform nonlinear prediction of the UAV flight dynamics andrelative moment between the transmitter and the receiver. A third stepin which Bayes optimal closed loop correction is performed.

Computer System

FIG. 12 is a block diagram of a computer system as may be used toimplement features of some of the embodiments. The computing system 1200may include one or more central processing units (“processors”) 1205,memory 1210, input/output devices 1225 (e.g., keyboard and pointingdevices, display devices), storage devices 1220 (e.g., disk drives), andnetwork adapters 1230 (e.g., network interfaces) that are connected toan interconnect 1215. The interconnect 1215 is illustrated as anabstraction that represents any one or more separate physical buses,point to point connections, or both connected by appropriate bridges,adapters, or controllers. The interconnect 1215, therefore, may include,for example, a system bus, a Peripheral Component Interconnect (PCI) busor PCI-Express bus, a HyperTransport or industry standard architecture(ISA) bus, a small computer system interface (SCSI) bus, a universalserial bus (USB), IIC (I2C) bus, or an Institute of Electrical andElectronics Engineers (IEEE) standard 1394 bus, also called “Firewire”.

The memory 1210 and storage devices 1220 are computer-readable storagemedia that may store instructions that implement at least portions ofthe various embodiments. In addition, the data structures and messagestructures may be stored or transmitted via a data transmission medium,e.g., a signal on a communications link. Various communications linksmay be used, e.g., the Internet, a local area network, a wide areanetwork, or a point-to-point dial-up connection. Thus, computer readablemedia can include computer-readable storage media (e.g., “nontransitory” media) and computer-readable transmission media.

The instructions stored in memory 1210 can be implemented as softwareand/or firmware to program the processor(s) 1205 to carry out actionsdescribed above. In some embodiments, such software or firmware may beinitially provided to the processing system 1200 by downloading it froma remote system through the computing system 1200 (e.g., via networkadapter 1230).

The various embodiments introduced herein can be implemented by, forexample, programmable circuitry (e.g., one or more microprocessors)programmed with software and/or firmware, or entirely in special-purposehardwired (non-programmable) circuitry, or in a combination of suchforms. Special-purpose hardwired circuitry may be in the form of, forexample, one or more ASICs, PLDs, FPGAs, etc.

Remarks

The above description and drawings are illustrative and are not to beconstrued as limiting. Numerous specific details are described toprovide a thorough understanding of the disclosure. However, in certaininstances, well-known details are not described in order to avoidobscuring the description. Further, various modifications may be madewithout deviating from the scope of the embodiments. Accordingly, theembodiments are not limited except as by the appended claims.

Reference in this specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiment is included in at least one embodimentof the disclosure. The appearances of the phrase “in one embodiment” invarious places in the specification are not necessarily all referring tothe same embodiment, nor are separate or alternative embodimentsmutually exclusive of other embodiments. Moreover, various features aredescribed which may be exhibited by some embodiments and not by others.Similarly, various requirements are described which may be requirementsfor some embodiments but not for other embodiments.

The terms used in this specification generally have their ordinarymeanings in the art, within the context of the disclosure, and in thespecific context where each term is used. Certain terms that are used todescribe the disclosure are discussed below, or elsewhere in thespecification, to provide additional guidance to the practitionerregarding the description of the disclosure. For convenience, certainterms may be highlighted, for example using italics and/or quotationmarks. The use of highlighting has no influence on the scope and meaningof a term; the scope and meaning of a term is the same, in the samecontext, whether or not it is highlighted. It will be appreciated thatthe same thing can be said in more than one way. One will recognize that“memory” is one form of a “storage” and that the terms may on occasionbe used interchangeably.

Consequently, alternative language and synonyms may be used for any oneor more of the terms discussed herein, nor is any special significanceto be placed upon whether or not a term is elaborated or discussedherein. Synonyms for certain terms are provided. A recital of one ormore synonyms does not exclude the use of other synonyms. The use ofexamples anywhere in this specification including examples of any termdiscussed herein is illustrative only, and is not intended to furtherlimit the scope and meaning of the disclosure or of any exemplifiedterm. Likewise, the disclosure is not limited to various embodimentsgiven in this specification.

Without intent to further limit the scope of the disclosure, examples ofinstruments, apparatus, methods and their related results according tothe embodiments of the present disclosure are given above. Note thattitles or subtitles may be used in the examples for convenience of areader, which in no way should limit the scope of the disclosure. Unlessotherwise defined, all technical and scientific terms used herein havethe same meaning as commonly understood by one of ordinary skill in theart to which this disclosure pertains. In the case of conflict, thepresent document, including definitions will control.

1-22. (canceled)
 23. A computer-implemented method, implemented at areceiver, for estimating a cross-polarization compensation, comprising:(a) defining a common orthogonal plane with respect to a transmitter;(b) pre-calibrating to an expected antenna depolarization angle; (c)estimating the transmitter's attitude and/or mapping with an antennatracking angle; (d) making, based on the estimating operation,corrections in horizontal and vertical polarization domains; (e)receiving a pilot signal from the transmitter; (f) estimating an amountof cross-polarization discrimination (XPD) based on the pilot signal;and (g) selectively iterating steps (c) to (g) to obtaincross-polarization compensation.
 24. The method of claim 23, wherein theestimating the transmitter's attitude includes setting an a priorichannel matrix as determined by a prior calculation.
 25. The method ofclaim 24, wherein the prior calculation includes an almanac table lookupor a past operation of a calibration method.
 26. The method of claim 23,wherein the estimating the amount of XPD includes: estimating ΔC_(r),A_(r) ^(T), H, and U; where A_(r) is the local base matrix, ΔC_(r) is across-depolarization matrix, U represents received corrupted datasignal, and H is an apriori channel matrix.
 27. The computer-implementedmethod of claim 23, wherein estimating the local cross-depolarizationmatrix comprises applying a maximum likelihood estimation of astatistical model.
 28. The computer-implemented method of claim 23,further including applying a post-correction channel condition toΔC_(r), A_(r) ^(T) and U.
 29. The computer-implemented method of claim28, wherein the applying the post-correction channel condition comprisesperforming a Bayesian update.
 30. A non-transitory computer-readablemedium comprising instructions configured to case at least one computerprocessor to estimate an original data signal from a corrupted datasignal received at two substantially orthogonally polarized antennas by:(a) defining a common orthogonal plane with respect to a transmitter;(b) pre-calibrating to an expected antenna depolarization angle; (c)estimating the transmitter's attitude and/or mapping with an antennatracking angle; (d) making, based on the estimating operation,corrections in horizontal and vertical polarization domains; (e)receiving a pilot signal from the transmitter; (f) estimating an amountof cross-polarization discrimination (XPD) based on the pilot signal;and (g) selectively iterating steps (c) to (g) to obtaincross-polarization calibration.
 31. The non-transitory computer-readablemedium of claim 30, wherein the estimating the transmitter's attitudeincludes setting an a priori channel matrix as determined by a priorcalculation.
 32. The non-transitory computer-readable medium of claim31, wherein the prior calculation includes an almanac table lookup or apast operation of a calibration method.
 33. The non-transitorycomputer-readable medium of claim 30, wherein the estimating the amountof XPD includes: estimating ΔC_(r), A_(r) ^(T), H, and U; where A_(r) isthe local base matrix, ΔC_(r) is a cross-depolarization matrix, Urepresents received corrupted data signal, and H is an apriori channelmatrix.
 34. The non-transitory computer-readable medium of claim 30,wherein estimating the local cross-depolarization matrix comprisesapplying a maximum likelihood estimation of a statistical model.
 35. Thenon-transitory computer-readable medium of claim 30, further includingapplying a post-correction channel condition to ΔC_(r), A_(r) ^(T) andU.
 36. The non-transitory computer-readable medium of claim 35, whereinthe applying the post-correction channel condition comprises performinga Bayesian update.
 37. A computer-implemented method, implemented at atransmitter, the method comprising: initializing a channel matrix H;performing an initial calibration and verification of an antenna of thetransmitter; calculating a depolarization angle from the initialcalibration and verification; predicting, based on available positioningsignals, an attitude of a receiver; determining an optimal nonlinearestimation of the depolarization angle based on the estimated attitudeof the receiver; processing a received training report and decisionbased on a training frame; and deciding whether to performcross-polarization training with the receiver.
 38. Thecomputer-implemented method of claim 37, wherein the initializing thechannel matrix H uses an almanac.
 39. The computer-implemented method ofclaim 37, wherein the cross-polarization training comprises transmittinga multi-input, multi-output (MIMO) channel training signal and anunmanned aerial system (UAS) attitude signal.
 40. A non-transitorycomputer-readable medium comprising instructions configured to cause atleast one computer processor to implement a wireless communicationmethod, the instructions comprising: code for initializing a channelmatrix H; code for performing an initial calibration and verification ofan antenna of the transmitter; code for calculating a depolarizationangle from the initial calibration and verification; code forpredicting, based on available positioning signals, an attitude of areceiver; code for determining an optimal nonlinear estimation of thedepolarization angle based on the estimated attitude of the receiver;code for processing a received training report and decision based on atraining frame; and code for deciding whether to performcross-polarization training with the receiver.
 41. The non-transitorycomputer-readable medium of claim 40, wherein the code for initializingthe channel matrix H includes code for using an almanac.
 42. Thenon-transitory computer-readable medium of claim 40, wherein the codefor the cross-polarization training comprises code for transmitting amulti-input, multi-output (MIMO) channel training signal and an unmannedaerial system (UAS) attitude signal.